Question: Simplify the following expression: $\dfrac{8n^3}{20n}$ You can assume $n \neq 0$.
Solution: $ \dfrac{8n^3}{20n} = \dfrac{8}{20} \cdot \dfrac{n^3}{n} $ To simplify $\frac{8}{20}$ , find the greatest common factor (GCD) of $8$ and $20$ $8 = 2 \cdot 2 \cdot 2$ $20 = 2 \cdot 2 \cdot 5$ $ \mbox{GCD}(8, 20) = 2 \cdot 2 = 4 $ $ \dfrac{8}{20} \cdot \dfrac{n^3}{n} = \dfrac{4 \cdot 2}{4 \cdot 5} \cdot \dfrac{n^3}{n} $ $\phantom{ \dfrac{8}{20} \cdot \dfrac{3}{1}} = \dfrac{2}{5} \cdot \dfrac{n^3}{n} $ $ \dfrac{n^3}{n} = \dfrac{n \cdot n \cdot n}{n} = n^2 $ $ \dfrac{2}{5} \cdot n^2 = \dfrac{2n^2}{5} $